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Denying the Antecedent and Affirming the Consequent

I am trying to learn and EASILY identify fallacy types... Deny the Consequent, Deny the Antecedent (invalid) etc.

Here are a few examples along with my initial response, but it doesn't appear that I got them right (although I don't know what the correct answer would be). Your assistance is greatly appreciated.

I thought this was Denying the Consequent:

If I master critical thinking then I will be a better employee
I am not a better employee
Therefore, I did not master critical thinking.

I thought this would be Deny the Antecedent:

If I can master critical thinking
then, I will be a better employee
I haven't mastered critical thinking
therefore I am not a better employee.

For the next statement I thought it contained two fallacies: Appeal to Ignorance and Appeal to Authority.

Rhymes' lawyer, Robert Kalina, told the judge, "I can tell you, judge, my client is innocent, and I rarely say this in a courtroom." He added that the accuser had no discernible injuries other than one red mark on his face.

Solution Preview

Please see attached file.

First it will be helpful to identify the parts of a conditional ("if ... then ...") statement. Symbolically we can represent any conditional statement as having the form:

A  B

Read this as "if A then B" (or, equivalently, as "A only if B"). In this statement the pro-position A is called the antecedent and the proposition B is called the consequent. It is easy to remember these labels if you think of cognate names. For "antecedent" think of "antecedes" as a synonym for "precedes," or what comes first/before. For "consequent," think of "consequence," or what follows from something that comes before. (You should also note that "antecedent" is a synonym for "sufficient condition," while "consequent" is a synonym for "necessary condition." So in the statement above, we would say A is sufficient for B. And we would say B is necessary for A.)

We use conditional statements in arguments or reasoning very frequently. So there are established names for some inferences involving conditional statements. For example the following two forms of reasoning are valid:

Modus Ponens (MP)
1. A  q
2. A
 3. B

Modus Tollens (MT)
1. A  B
2. ~B
 3. ~A

(Read the symbol '' as "therefore" and the symbol '~' as "not.")

In MP, notice that statement 2 affirms the antecedent of the conditional statement 1. Thus Modus Ponens is sometimes called "Affirming the Antecedent." Notice that in MT, statement 2 denies or negates the consequent of statement 1. Thus Modus Tollens is sometimes called "Denying the Consequent." Once again, both of these argument forms are valid. ...

Solution Summary

Explains the fallacies of "denying the antecedent" and "affirming the consequent." Compares these invalid forms of reasoning to the valid forms of Modus Ponens (affirming the antecedent) and Modus Tollens (denying the consequent). Provides examples of each. Also explains the reasoning involved in Hypothetical Syllogism.